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Certain very large cardinals are not created in small forcing extensions
2007
Annals of Pure and Applied Logic
The large cardinal axioms of the title assert, respectively, the existence of a nontrivial elementary embedding j : V λ → V λ , the existence of such a j which is moreover Σ 1 n , and the existence of such a j which extends to an elementary j : V λ+1 → V λ+1 . It is known that these axioms are preserved in passing from a ground model to a small forcing extension. In this paper the reverse directions of these preservations are proved. Also the following is shown (and used in the above proofs in
doi:10.1016/j.apal.2007.07.002
fatcat:coqlsq2xpnd2pdfkn56hjq7mji